Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints |
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| Authors: | Xinwei?Liu,Jie?Sun mailto:jsun@nus.edu.sg" title=" jsun@nus.edu.sg" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author |
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| Affiliation: | (1) Singapore-MIT Alliance, National University of Singapore and Department of Applied Mathematics, Hebei University of Technology, Tianjin, China;(2) School of Business and Singapore-MIT Alliance, National University of Singapore, Republic of Singapore |
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| Abstract: | ![]()
Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced under fairly general conditions other than strict complementarity or the linear independence constraint qualification for MPEC (MPEC-LICQ). It is shown that every limit point of the generated sequence is a strong stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a point with certain stationarity can be obtained. Preliminary numerical results are reported, which include a case analyzed by Leyffer for which the penalty interior-point algorithm failed to find a stationary point.Mathematics Subject Classification (1991):90C30, 90C33, 90C55, 49M37, 65K10 |
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| Keywords: | Global convergence Interior-point methods Mathematical programming with equilibrium constraints Stationary point |
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